Simulation of an Invetory Model by Stochastic Differential Equation Using sw Mathematica

The paper deals with stochastic dynamic inventory models which are solved numerically. An area of inventory theory research that has recently been receiving considerable attention involves situations in which the demand rate is dependent on the level of inventory. Inventory for an item is replenished by a time dependent deterministic process, in the simples case, with constant rate one. Simultaneously, the product under inventory is depleted by stochastic demand which rate depends upon the current inventory level. Stochastic differential equation of Ito type for the inventory level is formulated and used for numerical computations. All simulated paths of inventory levels are generated by our Mathematica code. Sample mean path is calculated thereof and further filtered in order to get some inventory management important values. Two main Mathematica commands for generation stochastic processes is presented, too.